I am not a realtor, but I've been through the process a few times, and I live in Palo Alto. The first thing I will tell you is that, if you wish to have any chance at success here, you have to work with a Palo Alto realtor. Marcy and Juliana are both well established here, as well as a number of others. Anyone who starts off by asking if I want a pool or other generic questions will not be on my short list.
Let me summarize the reality mentioned by others below. There are 3 main challenges when you wish to buy into this market:
1) Low to non-existent inventory at all times, and only a small subset of that will likely meet anyone's criteria and qualifications.
2) High prices is no exaggeration. Unless you are looking for projects, I suggest you make $2M as your minimum price target (after bidding)
3) Extremely high competition is also no exaggeration. Be prepared to bid against at least a dozen competitors.
If you need to stick to $1.5M as your price range, you need to consider other cities.
A final thought: You need a broker who well give you personal attention. Some of the bigger names will meet with you once and send you a junior staff to work with.